Apparatus and method to expand casing

ABSTRACT

A tool for radially plastically expanding a pipe having a threaded connection therein, that includes a first section. The first section has an increasing diameter and increasing cone angle along a direction of travel through the pipe. The first section includes a first outer surface adapted to contact an inner surface of the pipe at a plurality of selected contact patches on the first outer surface. The tool also includes a second section axially disposed behind the first section along the direction of travel. The second section has an increasing diameter and decreasing cone angle along the direction of travel. The second section includes a second outer surface adapted to contact an inner surface of the pipe at least one selected contact patch on the second outer surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 10/004,179, filed on Oct. 24, 2001, which issued as U.S. Pat.No. 6,622,799 on Sep. 23, 2003. That application is incorporated byreference in its entirety.

BACKGROUND OF INVENTION

[0002] 1. Field of the Invention

[0003] This invention relates generally to a device and method adaptedfor use with oilfield pipe (“tubulars”). More specifically, theinvention relates to a device and method used to plastically radiallyexpand downhole tubular members in a wellbore.

[0004] 2. Background Art

[0005] Casing joints, liners, and other oilfield tubulars are often usedin drilling, completing, and producing a well. Casing joints, forexample, may be emplaced in a wellbore to stabilize a formation, toprotect a formation against elevated wellbore pressures (e.g., wellborepressures that exceed a formation pressure), and the like. Casing jointsmay be coupled in an end-to-end manner by threaded connections, weldedconnections, and other connections known in the art. The connections maybe designed so as to form a seal between an interior of the coupledcasing joints and an annular space formed between exterior walls of thecasing joints and walls of the wellbore. The seal may be, for example,an elastomer seal (e.g., an o-ring seal), a metal-to-metal seal formedproximate the connection, or similar seals known in the art.

[0006] In some well construction operations, it is advantageous toradially plastically expand threaded pipe or casing joints in a drilled(“open”) hole or inside a cased wellbore. In a cased wellbore, radiallyexpandable casing can be used to reinforce worn or damaged casing so asto, for example, increase a burst rating of the old casing, therebypreventing premature abandonment of the hole. In open hole sections ofthe wellbore, the use of radially expandable casing may reduce arequired diameter of a drilled hole for a desired final cased holediameter, and may also reduce a required volume of cement required tofix the casing in wellbore.

[0007] In conventional oilfield drilling, casing strings are installedat regular intervals whereby the casing for the next interval isinstalled through the casing for the previous interval. This means thatthe outer diameter of a casing string is limited by the inner diameterof the previously installed casing string. Thus the casing strings in aconventional wellbore are nested relative to each other, with casingdiameters decreasing in a downward direction.

[0008] Conventionally, an annular space is provided between each stringof casing and the wellbore so that cement may be pumped into the annularspace or annulus to seal between the casing and the wellbore.

[0009] Because of the nested arrangement of the casing strings in aconventional wellbore, and the annular space required around the casingstrings for cement, the hole diameter required at the top of thewellbore is relatively large. This large initial wellbore diameter maylead to increased costs due to the expense of large diameter casing, theexpense of drilling large diameter holes, and the added expense ofcementing a large casing string.

[0010] In addition, the nested arrangement of the casing strings in aconventional wellbore can severely limit the inner diameter of the finalcasing string at the bottom of the wellbore, which restricts thepotential production rate of the well.

[0011] It is desirable that a casing string can be radially expanded insitu after it has been run into the wellbore through the previous casingstring, so as to minimize the reduction of inner diameter of the finalcasing string at the bottom of the wellbore. Radially expanding a casingstring in the wellbore has the added benefit of reducing the annularspace between the drilled wellbore and the casing string, which reducesthe amount of cement required to effect a seal between the casing andthe wellbore.

[0012] When a cold-forming expansion process is used (e.g., when acold-forming expansion tool or “pig” is moved through a casing string soas to radially plastically expand the casing string), the casing stringis usually run into the hole “box-down” (e.g., the “box” or femalethreaded connection is run into the hole facing downhole so that theexpansion tool (“pig”) does not deform the “pin” nose or male threadedconnection when the expansion tool is forced upward through the casingstring). Note that tubular strings such as drill pipe, casing, orsimilar tubular members are normally run into the hole “pin-down”because it is easier to make up the threaded connections in the tubularstring.

[0013] Various expandable casing techniques have already been developed.An expansion tool is typically used to plastically radially expand astring of casing or tubing disposed inside a wellbore from an initialcondition (e.g., from an initial diameter) to an expanded condition(e.g., with a larger diameter). One common prior-art expansion processuses a conically tapered, cold-forming expansion tool (commonly referredto as a “pig”) to expand casing in a wellbore. The expansion tool isgenerally attached to a lower end of a casing string that is run intothe wellbore. A leading mandrel of the expansion tool generallycomprises a cylinder with an external diameter that is less than a“drift” diameter of the made-up casing or tubing that is to be radiallyexpanded. The expansion tool includes a tapered section having a taperangle that is generally between 5 degrees and 45 degrees. The expansiontool is generally symmetric about a longitudinal axis thereof. Theexpansion tool also includes a cylindrical section having a diametertypically corresponding to a desired expanded inner diameter of a casingstring. The cylindrical section is followed by a tapered section.

[0014] After the casing string is set in place in the hole, usually byhanging-off the casing string from a casing hanger, a working string ofdrillpipe or tubing is run into the wellbore and attached to theexpansion tool (e.g., the working string is generally attached to theleading mandrel). The expansion tool may also comprise an axial boretherethrough (not shown) so that pressurized fluid (e.g., drillingfluid) may be pumped through the working string, through the expansiontool, and in to the wellbore so as to hydraulically pressurize thewellbore. Hydraulic pressure acts on a piston surface defined by a lowerend of the expansion tool, and the hydraulic pressure is combined withan axial upward lifting force on the working string to force theexpansion tool upward through the casing string so as to outwardlyradial displace the casing string to a desired expanded diameter. Inthis expansion process, a rate of radial expansion is determined by, forexample, a total plastic strain required to expand the casing string,the taper angle, and a rate of axial displacement of the expansion toolthrough the casing string. Consistency of the expansion process iscontrolled by transitions along the expansion tool and a cross-sectionalarea of, for example, lengths of casing that form the casing string,threaded connections that couple the length of casing, and the like.

[0015] The expansion tool may be inserted into the casing string ateither the bottom or the top, depending on the tool design and theapplication. Radial expansion may be performed at rates of, for example,25 to 60 feet per minute. Other expansion processes, such as expansionunder localized hydrostatic pressure, or “hydroforming,” are known inthe art, but are generally not used as much as the aforementionedcold-forming expansion process.

[0016] U.S. Pat. No. 5,348,095, issued to Worrall et al, discloses amethod of creating a wellbore in an underground formation. A borehole isdrilled in the underground formation, whereafter a casing of a ductilematerial is lowered into the borehole. The casing is selected to have asmaller elastic radial deformation than the surrounding formation whenthe casing is radially expanded against the borehole wall by applicationof a radial force to the casing. The radial force is applied to thecasing so as to radially expand the casing against the borehole wallthereby inducing a plastic radial deformation of the casing and anelastic radial deformation of the surrounding underground formation,whereafter the radial force is removed from the casing.

[0017] U.S. Pat. No. 5,667,011, issued to Gill et al, discloses a methodof creating a casing in a borehole formed in an underground formation.The method comprises the steps of (a) installing a tubular liner in theborehole, the liner being radially expandable in the borehole wherebythe liner in its radially expanded position has a plurality of openingswhich are overlapping in the longitudinal direction of the liner, (b)radially expanding the liner in the borehole, and (c) either before orafter step (b), installing a body of hardenable fluidic sealing materialin the borehole so that the sealing material fills the openings andthereby substantially closes the openings. The sealing material isselected so as to harden in the openings and thereby to increase thecompressive strength of the liner.

[0018] U.S. Pat. No. 6,012,523, issued to Campbell et al, discloses adownhole apparatus for use in expanding liner or tubing. The apparatuscomprises a body for connection to a string and an expansion portion onthe body. The expansion portion includes a plurality of radially movableparts for defining an outer surface thereof. The parts are initiallyarranged in an axially and circumferentially offset first configurationin which the parts may assume a smaller diameter first configuration.The apparatus is then run into a borehole and through a length ofexpandable tubing. The parts are then moved radially outwardly andaxially aligned such that the parts assume a larger diameter secondconfiguration and define a substantially continuous outer circumference.The expansion portion is then pulled through the tubing to expand thetubing.

[0019] U.S. Pat. No. 6,021,850, issued to Wood et al, discloses a methodand apparatus of expanding tubulars. In the preferred embodiment, arounded tubular is inserted through a larger tubular while suspended ona mandrel. A stop device, such as a liner hanger, is attached to thelarger tubular after delivery downhole on the mandrel. Upon engagementof the liner hanger or other stop device to the larger tubular, themandrel is freely movable with respect to the stop device. The mandrelcontains a deforming device such as a conically shaped wedge locatedbelow the tubular to be expanded. A force is applied from the surface tothe mandrel, pulling the wedge into the tubular to be expanded. When thewedge clears through the tubular to be expanded, it releases the stopdevice so that the stop device can be retrieved with the mandrel to thesurface. Thus, the stop device is supported by the larger tubing whilethe smaller tubing is expanded when the wedge is pulled through it.Should the tubular being expanded contract longitudinally while it isbeing expanded radially, it is free to move away from the stop device.

[0020] U.S. Pat. No. 6,029,748, issued to Forsyth et al, discloses anapparatus and method that allow for downhole expansion of long stringsof rounded tubulars, using a technique that expands the tubular from thetop to the bottom. The apparatus supports the tubular to be expanded bya set of protruding dogs which can be retracted if an emergency releaseis required. A conically shaped wedge is driven into the top of thetubing to be expanded. After some initial expansion, a seal behind thewedge contacts the expanded portion of the tubing. Further driving ofthe wedge into the tubing ultimately brings in a series of back-up sealswhich enter the expanded tubing and are disengaged from the drivingmandrel at that point. Further applied pressure now makes use of apiston of enlarged cross-sectional area to continue the furtherexpansion of the tubular. When the wedge has fully stroked through thetubular, it has by then expanded the tubular to an inside diameterlarger than the protruding dogs which formerly supported it. At thatpoint, the assembly can be removed from the wellbore. An emergencyrelease, involving dropping a ball and shifting a sleeve, allows,through the use of applied pressure, the shifting of a sleeve whichsupports the dog which in turn supports the tubing to be expanded. Oncethe support sleeve for the dog has shifted, the dog can retract to allowremoval of the tool, even if the tube to be expanded has not been fullyexpanded.

[0021] U.S. Pat. No. 6,085,838, issued to Vercaemer et al, discloses amethod of cementing a well permitting a reduction in the degree ofdiameter reduction of casing or liners required, and not requiringexcessively large initial conductor casing. The method is characterizedby provision of an enlarged wellbore and a novel liner structure whichis adapted for expansion of a reduced diameter section thereof downhole,providing, before expansion of the section, unimpeded flow of fluid fromthe enlarged wellbore during cementing and close fit of the expandedsection with the casing or preceding liner, after cementing is completedand expansion of the section. A novel well liner structure and novelwell liner expansion means are also disclosed.

SUMMARY OF THE INVENTION

[0022] In one aspect, the invention comprises a tool for radiallyplastically expanding a pipe having a threaded connection therein, thatincludes a first section. The first section has an increasing diameterand increasing cone angle along a direction of travel through the pipe.The first section includes a first outer surface adapted to contact aninner surface of the pipe at a plurality of selected contact patches onthe first outer surface. The tool also includes a second section axiallydisposed behind the first section along the direction of travel. Thesecond section has an increasing diameter and decreasing cone anglealong the direction of travel. The second section includes a secondouter surface adapted to contact an inner surface of the pipe at leastone selected contact patch on the second outer surface.

[0023] In another aspect, the invention comprises a method of expandingcasing comprising forcing a casing expansion tool through a casingsegment. The casing segment has a smaller inside diameter than a largestoutside diameter of the expansion tool. The expansion tool includes anouter surface, and a plurality of contact patches on the outer surface.The contact patches are adapted to contact a section of casing at aplurality of axial locations on the inside diameter of the casing.

[0024] In another aspect, the invention comprises a downhole apparatusincluding a casing expansion tool comprising an outer surface and aplurality of contact patches on the outer surface. Two adjacent contactpatches define two circumferential contact surfaces having two differentdiameters. The apparatus also includes a section of casing. An insidesurface of the section of casing is in contact with a plurality of thecircumferential contact surfaces of the casing expansion tool on atleast two axial locations.

[0025] Other aspects and advantages of the invention will be apparentfrom the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

[0026]FIG. 1 shows a partial cross section of a made-up prior arttubular threaded connection with wedge threads and a metal-to-metalinternal seal.

[0027]FIG. 2 shows a sectional view of a typical prior art conicalexpansion tool, beginning to deform casing pipe with a made-up tubularthreaded connection.

[0028]FIG. 3 shows a made-up tubular threaded connection with wedgethreads during the expansion by a prior art frustoconical expansiontool.

[0029]FIG. 4 shows the made-up tubular threaded connection of FIG. 3 inthe expanded state, that is, after the prior art expansion tool haspassed completely through the connection.

[0030]FIG. 5 shows a cross-sectional view of an embodiment of the casingexpansion tool of the current invention.

[0031]FIG. 5A shows a partial cross-sectional view of an embodiment ofthe casing expansion tool of the current invention.

[0032]FIG. 5B shows a cross section of another embodiment of the casingexpansion tool of the current invention entering a casing pipe.

[0033]FIG. 6 shows a partial cross-sectional view of an embodiment of afive-segment expansion tool of the current invention.

[0034]FIG. 7 shows a partial cross-sectional view of another embodimentof the expansion tool of the current invention.

[0035]FIG. 8 shows a partial cross-sectional view of another embodimentof the expansion tool of the current invention.

[0036]FIG. 9 shows a partial cross-sectional view of another embodimentof the expansion tool of the current invention.

[0037]FIG. 10 shows a partial cross-sectional view of another embodimentof the expansion tool of the current invention.

[0038]FIG. 11 shows a partial cross-sectional view of another embodimentof the expansion tool of the current invention.

DETAILED DESCRIPTION

[0039] The radial plastic expansion of made-up threaded connections onoilfield and other tubular goods may exhibit structural sealing problemsin the expanded threaded connections. Threaded connections that undergoradial expansion have a tendency to exhibit a non-uniform axialelongation and react differently to residual hoop stresses remainingafter radial expansion. Specifically, male (pin) threaded members andfemale (box) threaded members deform differently during radialexpansion. Depending on a direction of travel of the expansion tool(e.g., pin to box or box to pin), the second member to undergo radialexpansion will generally move away from the first member. Thisdifferential displacement phenomenon results in a loss of preload inaxially-engaged seals, making the use of conventional metal-to-metalseals (including, for example, shoulder seals) generally ineffective forplastically radially expanded casing and tubing.

[0040] When a joint of casing or tubing is radially plasticallyexpanded, a wall thickness of the casing joint and an overall axiallength of the casing joint are reduced by a process commonly referred toas “Poissoning,” and residual stresses are retained in the casing joint.At any given finite element proximate a middle of the casing joint, thecasing joint will maintain a substantially uniform diameter and wallthickness because each finite element experiences support from adjoiningfinite elements.

[0041]FIG. 1 shows a cross section of made-up tubular threadedconnection with wedge threads and a metal-to-metal internal seal of atype which is preferred for use on expandable casing. Wedge threads aregenerally dovetail shaped threads with converging thread crest width.Wedge threads are extensively disclosed in U.S. Pat. No. RE 30,647, U.S.Pat. No. RE 34,467, U.S. Pat. No. 4,703,954, and U.S. Pat. No.5,454,605, all assigned to the assignee of the current invention. Thismade-up connection consists of female box connection 100, and male pinconnection 101. The made-up connection has overall connection length 102(or the quantity L1) from pin nose 103 to box nose 104, and engagedthread length 105 (or the quantity L2) from the beginning of firstengaged thread on the pin 106 to the end of last engaged thread on thepin 107. Note that engaged thread length 105 cannot always be measuredin the same axial plane as implied by FIG. 1, as the start of the firstengaged thread will not always lie in the same axial plane as the end ofthe last engaged thread.

[0042] The wedge thread-form has stab flanks 108, so called because theygenerally come into contact when the threaded connection is initially“stabbed” together to be made-up. The thread-form also has load flanks109, so called because they carry tensile load exerted on a made-upconnection within a string of casing hanging in a wellbore. Thethread-form on pin connection 101 has pin thread roots 110 and pinthread crests 111 with pin thread crest width 114. The thread-form onbox connection 100 has box thread roots 112 and box thread crests 113.

[0043] Wedge threads are a suitable thread-form for expandable casingapplications because (a) their generally dovetail-shaped thread-formresists radial forces during and after expansion which might tend toseparate the pin connection from the box connection, and (b) becausethey may not make-up against a radial torque shoulder, but insteadtypically make-up by simultaneous contact of thread load flanks 109 andstab flanks 108. During the expansion process, axial strains in theconnection will often cause a radial torque shoulder to fail when thecompressive stresses at the shoulder exceed the compressive yieldstrength of the casing material. Other types of tubular threadedconnections can also be successfully used in expanded casingapplications with a tool and method according to the invention.

[0044] The made-up connection of FIG. 1 has an internal metal-to-metalseal area 115. This type of metal-to-metal seal is of a type taught byU.S. Pat. No. 5,423,579, issued to Blose et al. To achieve ametal-to-metal seal of this type, the two seal surfaces on the pin andbox must come together to form a thin cylindrical or frustoconicalcontact patch (commonly achieved in the current art there must be acertain minimum contact stress at the seal contact patch to effectsealing against internal pressure inside the casing. Conventionally,this contact stress may be developed during make-up when the pin and boxseal surfaces are axially forced together as the connection is threadedtogether (“made-up”) and the pin seal area is deflected slightlyinwards. This slight deflection creates a residual bending stress in thepin nose which in turn creates the contact stress at the seal contactpatch.

[0045]FIG. 2 is a sectional drawing of a typical prior art conicalexpansion tool 202 (or “expansion pig”), beginning to deform casing pipe260 with a made-up tubular threaded connection 250 consisting of boxconnection 200 and pin connection 201. The made-up tubular threadedconnection 250 has overall connection length 209 and engaged threadlength 208.

[0046] The conical expansion tool 202 and the made-up tubular threadedconnection 250 share a common center line 203. In this figure, conicalexpansion tool 202 is forced through the casing 260 in expansion tooldirection of travel 204.

[0047] Conical expansion tool 202 has cylindrical surface 210,frustoconical exit surface 211, and frustoconical expansion surface 205with cone angle 206 (labeled α) of approximately 10 degrees from axial,and an active length 207. The intersection of cylindrical surface 210and frustoconical expansion surface 205 forms inflection point 213.

[0048] Most prior art expansion tools have a cone angle larger than 10degrees. A shallow cone angle 206 is used in the example of the priorart shown in FIG. 2 to demonstrate that simply using a shallow coneangle 206 on a frustoconical expansion surface 205 may still presentdeficiencies of other prior art expansion tools having large cone angleswhen used to expand tubular threaded connections.

[0049] The active length 207 of the frustoconical expansion surface 205is defined as the axial length of the expansion surface 205 from theintersection with the inside surface of the casing 212 to the inflectionpoint 213 (the intersection of expansion surface 205 and cylindricalsurface 210). The active length 207 is therefore the section of thefrustoconical expansion surface 205 that bears on the inside surface ofthe casing 212 during the casing expansion process. It is characteristicof prior art expansion tools that the active length of the expansionsurface is quite short, typically in order to minimize the frictionbetween the expansion tool and the casing. Typically, the active length207 of the expansion surface is shorter than engaged thread length 208of the connection to be expanded.

[0050] In one embodiment of the invention, it has been discoveredthrough experimentation and Finite Element Analysis that tubularthreaded connections on expandable oilfield casing and the like whichare mechanically expanded as with a frustoconical expansion tool must beaxially supported during the expansion process, either by continuoussupport over the engaged thread length, or preferably at a number ofpoints within the engaged thread length. Some possible consequences ofusing an expansion tool which is too short to properly support thethreaded connection are illustrated in FIGS. 3 and 4.

[0051]FIG. 3 shows a made-up tubular threaded connection 350 with wedgethreads consisting of box connection 300 and pin connection 301, similarto the connection shown in FIG. 2, during the expansion by a prior artfrustoconical expansion tool (not shown) with the threaded section ofthe connection over the active length of the expansion tool. As iscommon practice in the prior art, the expansion tool proceeds inexpansion tool travel direction 302, from pin connection 301 to boxconnection 300, to avoid gross deformation of the pin nose 301A. Thisrequirement severely restricts the expansion operation, in that eitherthe expansion tool (not shown) must travel down the well (if the stringis run into the hole in the conventional manner, with the pin connectionfacing down) or the string must be run into the hole “box down” (whichis generally much slower, and therefore more expensive) to allow theexpansion tool (not shown) to travel up the well.

[0052] The box end 300A of the made-up connection 350 has already passedinflection point 308, which is the intersection of the frustoconicalexpansion surface 309 and cylindrical surface 310. Note that the lastengaged female thread 303 on the pin connection has “combed open”(so-called because the effect resembles the spreading of the teeth of acomb as it is bent backwards at its spine) and that the first engagedmale thread 304 on the box connection has experienced severe plasticdeformation in bending. Similar “combing” is beginning to occur at nextfemale thread 305 on the pin connection, which is directly adjacent toinflection point 308 on the expansion tool, and a large clearance gaphas formed at stab flank 306 of the second engaged male thread on thebox. Note that a clearance gap at stab flank 307 has already begun toform, even though there is not yet evidence at this point in theconnection of “combing.”

[0053]FIG. 4 shows made-up tubular threaded connection 450 of FIG. 3 inthe expanded state, that is, after the expansion tool (not shown) haspassed completely through the connection in expansion tool traveldirection 402. The made-up tubular threaded connection 450 consists ofbox connection 400 and pin connection 401.

[0054] The last engaged female thread 403 of the pin connection 401 hasexperienced significant axial strain as a result of the “combing”induced by the expansion tool. The first engaged male thread 404 of thebox connection 400 exhibits the plastic deformation in bending seen inFIG. 3. As a result, these threads have essentially no stab flankcontact and greatly reduced load flank contact. The next engaged malethread 408 of the box connection 400 shows similar plastic deformationin bending, which contributes to a large clearance gap at the load flank407. The next engaged male thread 410 of the box connection 400 showsslightly less plastic deformation in bending, but still has asignificant clearance gap at the corresponding load flank 409.

[0055] Similarly, last engaged female thread 406 of the box connection400 exhibits plastically enlarged thread width, while first engaged malethread 405 of the pin connection 401 exhibits plastic deformation inbending, resulting in a very large load flank clearance gap 411.

[0056] In addition, pin nose 401A will typically be slightly radiallydeformed inward, reducing the contact stress at metal-to-metal seal 412.Expansion with a prior art expansion tool, particularly an expansiontool with a simple frustoconical expansion surface, usually causes themetal-to-metal seal to begin to leak during the expansion process. Thiscan be a critical limitation for those expansion processes which rely onfluid pressure behind the expansion tool to help propel the tool. Usingprior art expansion processes to expand a tubular threaded connectionwith a metal-to-metal seal, it is unlikely that the metal-to-metal sealwill survive the expansion process intact.

[0057] A possible result of these deformations in a tubular threadedconnection caused by prior art expansion methods is that (a) theefficiency of the connection (commonly defined as the ratio of amechanical property of the pipe body, such as axial tension capacity, tothe same mechanical property across the connection) may drop severelyafter casing expansion, despite the fact that the pipe body wallthickness is generally reduced during the expansion process, thusreducing the mechanical properties of the pipe body itself, and (b)metal-to-metal seals may not survive the expansion process.

[0058]FIG. 5 shows a cross-section of an embodiment of a casingexpansion tool 500 of the current invention. Expansion tool 500 isaxi-symmetric about center-line 501, has first chamfer 502 with chamferangle 502A, and last chamfer 503, overall length 504,length-less-chamfers 505, and expansion tool direction of travel 510.Length-less-chamfers 505 is divided into four sections: first expansionsection 506, second expansion section 507, cylindrical section 508, andtail section 509.

[0059] First expansion section 506 in this embodiment is further dividedinto four substantially equal-length frustoconical expansion segments506A through 506D, each with a different cone angle, and separated byradius intervals 511A through 511C.

[0060] Expansion segment 506A has included angle 513A of approximately177.5 degrees from cylindrical plane 515, equivalent to a cone angle β515A of 2.5 degrees. The cone angle β 515A is the angle formed by theintersection of cylindrical plane 515 and the outer surface 550 ofexpansion segment 506A. The included angles 513B through 513D betweenadjacent expansion segments 506A through 506D are also approximately177.5 degrees in this embodiment of the current invention. That is, thecone angle for expansion segment 506B is approximately 5.0 degrees (theangle formed by the intersection of cylindrical plane 515 and the outersurface 551 of expansion segment 506B), the cone angle for expansionsegment 506C is approximately 7.5 degrees (the angle formed by theintersection of cylindrical plane 515 and the outer surface 552 ofexpansion segment 506C), and the cone angle for expansion segment 506Dis approximately 10.0 degrees (the angle formed by the intersection ofcylindrical plane 515 and the outer surface 553 of expansion segment506D). In the first expansion section 506 of this embodiment, eachsegment has a cone angle that is 2.5 degrees greater than the previoussegment.

[0061] Second expansion section 507 is further divided into threesubstantially equal-length frustoconical expansion segments 507A through507C, each with a different cone angle, and separated by radiusintervals 511E and 511F. In the second expansion section 507 of thisembodiment, each segment has a cone angle that is 2.5 degrees less thanthe previous segment.

[0062] First expansion section 506 and second expansion section 507 areseparated by inflection plane 516 which lies at the midpoint of radiusinterval 511D. The included angle 514A between expansion segments 506D(the last expansion segment in first expansion section 506) andexpansion segment 507A (the first expansion segment of second expansionsection 507) is approximately 182.5 degrees in this embodiment. The coneangle of expansion segment 507A is therefore approximately 7.5 degrees.

[0063] The included angles 514B and 514C between adjacent expansionsegments 507A through 507C, and included angle 514D between expansionsegment 507C and cylindrical segment 508A, are also all approximately182.5 degrees in this embodiment of the current invention. That is, thecone angle for expansion segment 507B is approximately 5.0 degrees, andthe cone angle for expansion segment 507C is approximately 2.5 degrees.

[0064] Generally, expansion segments 506A through 506D within firstexpansion section 506 form a “concave” surface, that is, eachfrustoconical expansion segment in first expansion section 506 has alarger cone angle than the preceding segment. Generally, expansionsegments 507A through 507C within second expansion section 507 form a“convex” surface, that is, each frustoconical expansion segment insecond expansion section 507 has a smaller cone angle than the precedingsegment.

[0065] In one embodiment, it has been determined from modeling andexperimentation that the cone angle β 515A of first expansion segment506A of the first expansion section 506 should be between about 2degrees and about 6 degrees, and that the included angle betweenadjacent expansion segments should be between about (180°−β) and(180°+β).

[0066] Radius intervals 511A through 511C may be included to provide aradiused transition from one expansion segment to the next, followingconventional machining practice. See FIG. 5A, which shows a partialcross section of expansion tool 500 shown in FIG. 5, and expanded viewsof radius interval 511A (between expansion segments 506A and 506B) andof radius interval 511D, between expansion segments 506D and 507A. Inthis embodiment of the current invention, radius intervals 511A through511C have concave radii of curvature of about 2 inches, which yields asmooth transition from one expansion segment to the next, but which hasan axial length which is less than one tenth of the axial length of theneighboring expansion segments. By contrast, radius intervals 511Dthrough 511G have convex radii of curvature of about 2 inches.

[0067]FIG. 5B shows a cross section of an embodiment of the expansiontool 500 of the current invention entering a casing or pipe 517 to beexpanded. In this embodiment, first chamfer 502 has chamfer angle 502Awhich matches the chamfer angle on pipe chamfer 517A, and the axiallength of first chamfer 502 is longer than the first chamfer shown inFIG. 5 and FIG. 5A. These modifications ensure that the tool 500 willpilot inside the casing 517 when starting the expansion process.

[0068] In addition, first expansion segment 506A of first expansionsection 506 is about twice the length of each of the other expansionsegments 506B through 506D and 507A through 507C. The first diameter 518of expansion segment 506A is determined so that the nominal ID of casing517 will contact the surface of expansion segment 506A at first contactplane 519, which is located approximately halfway along the surface ofexpansion segment 506A. That is, the length of segment 506A aftercontact plane 519 is approximately the same as the length of the otherexpansion segments. These features ensure that expansion segment 506Acan be stabbed deeply into the casing 517 to be expanded, but thatallowance has been made for variation in pipe ID from its nominal ID.

[0069] Referring again to FIG. 1, when expansion tool 500 is forcedthrough casing, one would expect that the casing ID will be expanded toa new diameter which is the same as the largest diameter of expansiontool 500, namely the diameter of cylindrical section 508. However, inpractice, frustoconical-type expansion tools are typically moved throughsolid casing or expanded metal screens as quickly as possible, with theresult that the casing ID usually expands to a diameter larger than thelargest diameter of the expansion tool used. This additional amount ofexpansion is conventionally called “surplus” expansion. This surplusexpansion may be caused by differential stresses created by theexpansion process. The amount of surplus expansion seems to depend onthe design of the expansion tool, the coefficient of friction betweenthe tool and the casing, and the rate of application of the tool to thecasing. At the current state of the art, the amount of surplus expansionis most economically determined in an empirical fashion, by testingparticular combinations of expansion tools and tubular goods atdifferent rates of expansion tool travel.

[0070] Expansion tool 500 is designed for a particular application byfirst establishing the following variables:

[0071] nominal ID of the unexpanded casing pipe

[0072] expanded ID of the expanded casing pipe

[0073] diametrical surplus expansion expected

[0074] L2=engaged thread length 105 (in FIG. 1) of the tubular threadedconnection

[0075] Diameter of the expansion tool of this embodiment of the currentinvention at first contact plane 519 in FIG. 5B is designed to be equalto the nominal ID of the unexpanded casing pipe 517.

[0076] The diameter of the cylindrical section 508 in FIG. 5B isdesigned to be equal to the expanded ID of the expanded casing, less thediametrical surplus expansion.

[0077] The difference between the diameter of the first contact plane519 in FIG 5B and the diameter of the cylindrical section 508 in FIG 5Bis the required diametrical change in the expansion tool 500.

[0078] In one embodiment, the axial length of each expansion segmentwithin first expansion section 506 and second expansion section 507 hasbeen determined by experiment to be between about L2 (engaged threadlength 105 in FIG. 1), and about 0.1 L2 (or, one-tenth of the engagedthread length). In another embodiment, the axial length of eachexpansion segment within first expansion section 506 and secondexpansion section 507 has been determined by experiment to be betweenabout 0.8 L2, and about 0.2 L2. In another embodiment, the axial lengthof each expansion segment within first expansion section 506 and secondexpansion section 507 has been determined by experiment to be betweenabout 0.5 L2, and about 0.25 L2.

[0079] In one embodiment, the combined length of the first expansionsection 506 and second expansion section 507 must be at least about L2(engaged thread length 105 in FIG. 1).

[0080] In one embodiment, all of the expansion segments are of equalaxial length. In another embodiment, all of the expansion segments areof equal axial length with the exception of the first expansion segment506A of the first expansion section 506, which can be made longer tofacilitate stabbing the expansion tool into the casing, as shown in FIG.5B. Longer axial length of the expansion segments may increase thefriction between the expansion tool and the casing, and may result in asmaller surplus expansion. Shorter axial length of the expansionsegments may reduce the friction between the expansion tool and thecasing during the expansion process, but may result in a larger surplusexpansion.

[0081] In another embodiment, each expansion segment may have adifferent axial length in order to make the contact patches have auniform length. Generally, as the cone angle increases, the length ofthe contact patch increase. In order to equalize the length of thecontact patches, the segments with a higher cone angle would have ashorter axial length, while the segments with a lower cone angle wouldhave a longer axial length.

[0082] A “step-angle” between about 2 degrees and about 6 degrees may beselected. This step angle will be the cone angle of the first expansionsegment 506A and the absolute value of the change in angle betweencontiguous expansion segments. For example, the included angle betweenthe expansion segments in first expansion section 506 in FIG. 2 is 177.5degrees, so that the step angle is 2.5 degrees, or the absolute value of180 degrees minus the included angle. It has been found by FiniteElement Analysis that the step angle for moderate casing expansions,typically between 10-15%, may be from about 2 to about 2.5 degrees.

[0083] A total number of expansion segments is selected, which may be anodd integer. In most cases of casing expansion, it has been found thatabout 7 or about 9 expansion segments may be practical, although it ispossible to design a serviceable tool with more or fewer segments.

[0084] The following equations relate the expansion segment length, thestep angle, and the total number of segments to the required diametricalchange in the expansion tool. For each segment:

H=L tan β

[0085] where:

[0086] H=radial height of segment

[0087] L=axial length of segment

[0088] β=step angle

[0089] For an expansion tool with seven expansion segments, this yields

H1=Ltanβ+Ltan2β+Ltan3β+Ltan4β

H2=Ltanβ+Ltan2β+Ltan3β

[0090] and

HTOTAL=H1+H2

[0091] where

[0092] H1=radial height of First Expansion Section

[0093] H2=radial height of Second Expansion Section

[0094] HTOTAL=total radial height of the expansion tool

[0095] Which yields

HTOTAL=Ltanβ+Ltan2β+Ltan3β+Ltan4β+Ltan β+Ltan 2β+Ltan3β

HTOTAL=2L (tanβ+tan2β+tan3β+½ tan4β)

DTOTAL=4L (tanβ+tan2β+tan3β+½ tan4β)

[0096] where

[0097] HTOTAL=total radial height of expansion tool

[0098] DTOTAL=total diametrical change in expansion tool

[0099] For example, if it is desired to expand a 7⅝ inch OD oilfieldcasing pipe with a nominal ID of 6.875 inches, to an expanded ID of atleast 8.005 inches (an expansion of 16%), an expansion tool according tothe embodiment of the current invention shown in FIG. 2 could bedesigned as follows:

[0100] The first contact plane 519 in FIG. 5B should be 6.875 inches,the ID of the unexpanded 7⅝ inch, 29.70 pound per foot casing.

[0101] Assuming a surplus expansion (established empirically byexperimentation) of about 1%, the diameter of the cylindrical section508 in FIG. 2 should be 8.005 inches less 1%, or 7.925 inches.

[0102] The total diametrical change required in the expansion tool istherefore 1.050 inches.

[0103] For an expansion tool with seven expansion stages and a stepangle of 2 degrees (β=2 degrees) the segment length is calculated asfollows:

DTOTAL=4L (tanβ+tan2β+tan3β+½ tan4β)

1.050=4L (tan 28+tan 48+tan 68 +½ tan 88)

1.050=4L (0.280)

L=1.050/1.120=0.937 inches

[0104] For a threaded connection with an engaged thread length (L2) of 3inches, a segment length of 0.937 inches represents 0.312 L2, within therange for expansion segment length of 0.25 L2 to 0.5 L2.

[0105]FIG. 6 shows a cross-sectional view of a five-segment expansiontool which is another embodiment of the current invention. In thisembodiment, the cone angles and the changes in cone angles betweensegments are much larger than the equivalent angles of the embodimentsshown in FIGS. 5, 5A, and 5B. This means that the included anglesbetween expansion segments 605A through 605C are much smaller, andincluded angles between expansion segments 605C, 606A and 606B are muchlarger, than the equivalent angles of the embodiments shown in FIGS. 5,5A, and 5B. These angles are exaggerated in the view of FIG. 6 primarilyfor the purposes of clarity.

[0106] Expansion tool 600 has center-line 601, first chamfer 602, lastchamfer 603, and expansion tool travel direction 604. Total 600 also hasfirst expansion section 605, second expansion section 606, cylindricalsection 607, and tail section 608.

[0107] First expansion section 605 is divided into three expansionsegments 605A through 605C, each with a different cone angle. Forpurposes of clarity, no radius intervals are shown between the expansionsegments. Second expansion section 606 is divided into two segments 606Aand 606B.

[0108] Expansion segment 605A has a cone angle 608A of 12 degrees fromcylindrical plane 609. Expansion segment 605B has cone angle 608B of 24degrees, and expansion segment 605C has a cone angle 608C of 36 degrees.In the second expansion section 606, expansion segment 606A has coneangle 611A of 24 degrees, and expansion segment 606B has cone angle 611Bof 12 degrees. First expansion section 605 and second expansion section606 are separated by inflection plane 610.

[0109] Casing 612 is shown during the process of expansion. As theexpansion tool passes through the casing pipe, the casing pipe shows thecharacteristic surplus expansion 613, which is the difference betweenthe ID of the expanded casing pipe and the largest OD of the expansiontool, namely the diameter of cylindrical section 607.

[0110] Expansion segments 605B, 605C, 606A, and 606B are allapproximately the same axial length, while expansion segment 605A isapproximately twice as long as the other expansions, as in theembodiment of the current invention shown in FIG. 5B, in order to easeentry into the casing pipe. Alternatively, expansion segments 605B,605C, 606A, and 606B may have varying lengths in order to equalize thelength of the contact patches 614A through 614E as discussed above.

[0111] The large cone angles of the expansion segments on the expansiontool shown in FIG. 6 allow one to clearly see the contact patches 614Athrough 614E between casing pipe 612 and expansion tool 600. Note thatthe contact patches 615A through 615C in first expansion section 605occur near the middle of their respective expansion segments, whilecontact patches 614D and 614E in second expansion section 606 occur atthe inflection planes between the segments. Contact patch 614C, whichoccurs immediately before inflection plane 610 is characteristicallyaxially longer than the other contact patches, and clearance gap 615C,immediately after inflection plane 610, is axially longer than the othercontact patches.

[0112]FIG. 6 shows many of the important elements of the currentinvention. A plurality of contact patches provide support under thethreaded tubular connection during the expansion process. In oneembodiment, there are at least two contact patches. In anotherembodiment, there are at least three contact patches. In anotherembodiment, there are at least four contact patches. Relatively smallincluded angles between the expansion stages limit the strain rateimposed on the casing pipe. The expansion tool has two distinct sectionsof expansion stages: the first section is nominally “concave”, that is,the included angle between stages within the first section is less than180 degrees. The second section is nominally “convex”, that is, theincluded angle between stages within the second section is greater than180 degrees. Clearance gaps between the contact patches both reducefriction between the expansion tool and the expanding pipe, and it isbelieved, allow the stresses in the expanding casing to equalize orequilibrate through the entire thickness of the pipe body and thetubular threaded connection during expansion.

[0113] Design of prior art expansion tools has followed the intuitiveprinciple that the profile of the expansion tool should be in contactwith the expanding casing pipe as long as possible, consistent withlimiting the friction between the expansion tool and the casing pipe tocontrol the expansion force required. It has been discovered throughFinite Element Analysis and experimentation, however, that anuninterrupted expansion tool profile may result in large differencesbetween residual stresses at the OD of the pipe and residual stresses atthe ID of the pipe. These differential residual stresses are generallynot deleterious in the pipe body, but may inevitably cause the failureof threaded tubular connections at the end of a pipe joint, where theresidual stresses can not be relieved by a neighboring pipe-bodyelement, but must be relieved through the threaded tubular connection.It has been demonstrated that even the best available wedge threadconnection may not tolerate moderate radial plastic expansion (on theorder of 10 per cent or greater) by a full-contact expansion tool of theprior art without failure of the connection and/or the metal-to metalseal.

[0114]FIG. 7 shows a cross-section of another embodiment of theexpansion tool of the current invention. Expansion tool 700 hasexpansion surface profile 703, cylindrical section 706, first expansionsection 701 with expansion segment 701A through 701C, and secondexpansion section 702 with expansion segments 702A and 702B. Firstexpansion section 701 and second expansion section 702 are separated byinflection plane 705. Each expansion segment has a frustoconical contactplane 704A through 704C and 706A and 706B. The nominal contact planesare tangential to the contact patch on the surface of each expansionsegment. The expansion surface profile 703 is radially relieved (or“cut-back”) between the contact patches to form radial relief grooves707A through 707D. In this embodiment, the relief grooves form an acuteangle at their roots.

[0115] For example, contact plane 704A has a cone angle 707 of 6degrees, and intersects contact plane 704B, which has a cone angle of 12degrees, at plane 708 separating expansion elements 701A and 701B. Inturn, contact plane 704C has a cone angle of 18 degrees, contact plane706A has a cone angle of 12 degrees, and contact plane 706B has a coneangle of 6 degrees.

[0116] Essentially, the contact planes are “ghost” tangential surfaceswhich describe an embodiment of the current invention in which theexpansion elements are a series of contiguous frustoconical surfaces.The embodiment shown in FIG. 7 can in fact be created by machining-awaythe expansion surface profile described by the contact planes until theshape of contact surface profile 703 is achieved, preserving the contactpatches intact, but radially relieving the clearance gaps.

[0117]FIG. 8 shows another embodiment of the current invention similarto that shown in FIG. 7. Expansion tool 800 has expansion segments 801Athrough 801C, and 802A and 802B, and contact planes 803A through 803C,and 804A and 804B. Cone angles for the contact planes in this embodimentare the same as for the embodiment shown in FIG. 7. However, in thisembodiment, radial relief grooves 805A through 805D are smooth troughs.

[0118]FIG. 9 shows another embodiment of the expansion tool of thecurrent invention. This is a multi-part expansion tool which consists ofa central shaft 900 about which are positioned a series of disks ofvarying profiles. Expansion die disks 901A through 901D have contactpatches tangential to contact planes 902A through 902D. In oneembodiment, the expansion die disks may be made from a very hard anddurable material with a low coefficient of friction when used incold-forming steel, for example a microgram tungsten carbide, or aceramic material. Spacer spools 903A through 903E serve to axiallyposition and support the expansion die disks on the central shaft. Thedisks may be secured on the shaft by any conventional means, includingthreaded end caps or shear pins, for example. This embodiment has theadvantage that a relatively small inventory of die disks and spacerspools can be used to assemble a large range of expansion tools, thatcertain variables (such as the surplus expansion ratio) can befield-adjusted, and that individual die disks can be replaced orrepaired rather than repairing an entire tool.

[0119]FIG. 10 shows another embodiment in which the surfaces ofball-bearings are used to provide contact patches along the length of anexpansion tool. Expansion tool 1000 is divided into first expansionsection 1001, second expansion section 1002, and cylindrical section1003. First expansion section 1001 has expansion segments 1001A through1001C. Second expansion section 1002 has expansion segments 1002A and1002B. Ball bearings 1005 are mounted in expansion tool body 1000 suchthat the surface of the ball bearing is tangential to the contactplanes. This embodiment has the advantage that friction between theexpansion tool and the casing pipe during the expansion process can begreatly reduced, and that the tool may be easily rotated as it isadvanced. Depending on the helix angle described by a ball bearing asthe expansion tool is rotated and advanced through the casing pipe atthe same time, rotating the tool can yield a much lower effective coneangle than straight axial advancement of the expansion tool. In oneembodiment, if the helix angle is known with some precision, that is, ifthe rate of axial travel and rate of rotation are both known, the ballbearings can be helically staggered around the circumference such thatthe circumferential gap between the balls is minimized. In anotherembodiment, the ball bearings can be circumferentially located aroundthe tool.

[0120]FIG. 11 shows another embodiment which uses expansion rollers1102A through 1102D mounted in expansion tool 1100 such that the radialsurface of the rollers follows the contact planes 101A through 101E.Expansion tool 1000 has first expanding section 1103 and secondexpansion section 1104. The expansion rollers are located axially suchthat they form the contact patches of the expansion tool. Expansionrollers 1102A and 1102B, in first expansion section, are located nearthe middle of an expansion segment, and have simple frustoconicalprofiles with cone angles equal to the cone angles of their associatedcontact planes. Expansion rollers 1102C and 1102D, in second expansionsecond, are located between expansion segments, and have compoundfrustoconical profiles with an obtuse included angle.

[0121] In one embodiment, the tool of this invention is lowered into aborehole and then pulled and/or forced up the borehole by fluid pressurein order to expand the casing. Pulling and/or forcing a tool up aborehole to expand casing is known in the art.

[0122] In another embodiment, the tool of this invention is pushedand/or forced down the borehole by fluid pressure in order to expand thecasing, and then retrieved or abandoned. Pushing and/or forcing a tooldown a borehole to expand casing is known in the art.

[0123] In one embodiment, the tool of this invention is a static singlepiece of material, for example steel, that has been machined and/orformed to achieve the desired shape to expand casing.

[0124] In another embodiment, the tool of this invention is made up aplurality of radially movable parts for defining an outer surfacethereof as disclosed in U.S. Pat. No. 6,012,523, issued to Campbell etal. The plurality of radially movable parts would be formed so as toform a plurality of contact patches, for example 2, 3, 4, 5, 6, or 7, asdiscussed above.

[0125] In another embodiment, the tool of this invention includes ahydraulic mechanism that can serve to expand and/or contract the tool.The tool could be expanded before being used to expand casing, and thetool could be contracted before being run through casing in anunexpanded state. In another embodiment, the tool of this inventionincludes a mechanical mechanism and/or an electromechanical mechanismthat can serve to expand and/or contract the tool.

[0126] In another embodiment, the tool is made up of a number of piecesthat can be collapsed and/or disassembled in order to allow the tool tofit through shall diameter orifices. In addition, the pieces can beexpanded and/or reassembled prior to being used to expand casing.

[0127] It will be apparent to those skilled in the art that theexpansion tool of the current invention can assume many different shapesother than a monolithic “pig” with frustoconical segments.

[0128] Advantages of the invention may include one or more of thefollowing:

[0129] A mechanical expansion technique that is reliable and/orrelatively inexpensive;

[0130] An expansion tool having the ability to radially deform tubularthreaded connections, which are conventionally used to join togethersegments (“joints”) of casing pipe into a long string, withoutsignificantly weakening the load-carrying capacity of the threadedconnection, and/or without destroying the metal-to-metal seals commonlyrequired in such threaded connections; and

[0131] An expansion tool that generates relatively low friction forcesbetween the tool and the casing during the expansion process.

[0132] While the invention has been described with respect to a limitednumber of embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

What is claimed is:
 1. A tool for radially plastically expanding a pipehaving a threaded connection therein, comprising: a first section havingan increasing diameter and increasing cone angle along a direction oftravel through the pipe, the first section comprising a first outersurface adapted to contact an inner surface of the pipe at a pluralityof selected contact patches on the first outer surface; and a secondsection axially disposed behind the first section along the direction oftravel, the second section having an increasing diameter and decreasingcone angle along the direction of travel, the second section comprisinga second outer surface adapted to contact the inner surface of the pipeat least one selected contact patch on the second outer surface.
 2. Thetool of claim 1, wherein the first section comprises three contactpatches, said three contact patches defining a concave profile of thefirst outer surface, and wherein the second section comprises twocontact patches, said two contact patches defining a convex profile ofthe second outer surface.
 3. The tool of claim 1, wherein the first andsecond sections comprise a plurality of frustoconical elements.
 4. Thetool of claim 3, wherein each frustoconical element in the first sectionhas a cone angle and axial length selected so that at most one contactpatch is disposed on each frustoconical element in the first section. 5.The tool of claim 1, further comprising a plurality of radial reliefgrooves on the first and second outer surfaces between said contactpatches.
 6. The tool of claim 5, wherein at least one of the radialrelief grooves comprises an acute angle at a root of said groove.
 7. Thetool of claim 6, wherein at least one of the radial relief groovescomprises a smooth trough.
 8. The tool of claim 1, further comprising aplurality of disks, wherein said selected contact patches are located onsaid disks.
 9. The tool of claim 8, wherein the disks comprise at leasttwo different profiles.
 10. The tool of claim 9, further comprising atleast one spacer between at least two of said disks.
 11. The tool ofclaim 1, further comprising a plurality of ball bearings on the firstand second outer surfaces, wherein said selected contact patches arelocated on said ball bearings.
 12. The tool of claim 11, wherein saidball bearings are arranged helically about at least one of said firstouter surface and said second outer surface.
 13. The tool of claim 12,wherein said ball bearings are arranged circumferentially about at leastone of said first outer surface and said second outer surface.
 14. Thetool of claim 1, further comprising a plurality of expansion rollers,wherein said contact patches are located on said expansion rollers. 15.The tool of claim 1, wherein the first and second sections comprise aplurality of elements each defining a cone angle, a first element havinga cone angle between about 2 and about 6 degrees, an included anglebetween adjacent segments being between about 174 and about 186 degrees.16. The tool of claim 1, wherein the first and second sections comprisea plurality of frustoconical elements each defining a cone angle, achange in angle between each element being between about 2 degrees andabout 2.5 degrees.
 17. A method of expanding casing comprising forcing acasing expansion tool through a casing segment, wherein the casingsegment has a smaller inside diameter than a largest outside diameter ofsaid expansion tool; wherein said expansion tool comprises a firstsection having an increasing diameter and increasing cone angle along adirection of travel through the casing segment, the first sectioncomprising a first outer surface adapted to contact an inner surface ofthe casing segment at a plurality of selected contact patches on thefirst outer surface; and a second section axially disposed behind thefirst section along the direction of travel, the second section havingan increasing diameter and decreasing cone angle along the direction oftravel, the second section comprising a second outer surface adapted tocontact an inner surface of the pipe at least one selected contact patchon the second outer surface.
 18. A tool for radially plasticallyexpanding a pipe having a threaded connection therein, the connectionhaving an engaged thread length L2, the tool comprising: a first sectionhaving an increasing diameter and increasing cone angle along adirection of travel through the pipe, the first section comprising afirst outer surface adapted to contact an inner surface of the pipe at aplurality of selected contact patches on the first outer surface; and asecond section axially disposed behind the first section along thedirection of travel, the second section having an increasing diameterand decreasing cone angle along the direction of travel, the secondsection comprising a second outer surface adapted to contact the innersurface of the pipe at least one selected contact patch on the secondouter surface; wherein the first and second section have a length atleast about L2.
 19. The tool of claim 18, wherein the first and secondsections further comprise a plurality of expansion segments, and each ofsaid contact patches is located on one of said expansion segments. 20.The tool of claim 19, wherein each of said expansion segments has alength between about 0.1*L2 and L2.
 21. The tool of claim 20 whereineach of said expansion segments has a length between about 0.2*L2 and0.8*L2.
 22. The tool of claim 21, wherein each of said expansionsegments has a length between about 0.25*L2 and 0.5*L2.
 23. The tool ofclaim 20, wherein a first of said expansion segments of said firstsection has a length at least about twice the length of an averagelength of the other expansion segments of the first and second sections.24. A tool for radially plastically expanding a pipe having a threadedconnection therein, comprising: a section having an increasing diameterand increasing cone angle along a direction of travel through the pipe,the section comprising an outer surface adapted to contact an innersurface of the pipe at a plurality of selected contact patches on theouter surface.
 25. A method of expanding casing comprising forcing acasing expansion tool through a casing segment axially and rotating saidtool about a longitudinal axis of said tool, wherein the casing segmenthas a smaller inside diameter than a largest outside diameter of saidexpansion tool; wherein said expansion tool comprises a first sectionhaving an increasing diameter and increasing cone angle along adirection of travel through the casing segment, the first sectioncomprising a first outer surface adapted to contact an inner surface ofthe casing segment at a plurality of selected contact patches, eachcontact patch comprising a plurality of ball bearings.